Quantum study of Foldy--Wouthuysen--Tani theory on lattice

We study here a quantum version of Foldy--Wouthuysen--Tani (FWT) transformation and compare the similarities and differences between the quantum and the classic FWT theories. Then the improvement of action on lattice is discussed. The result shows that it is not necessary to improve the covariant difference along the time direction on lattice. Finally we discuss briefly the structure of physical vacuum and give a model independent of field condensate.